Influence of Bearing Clearance on Load Sharing in Planetary Gears

Load sharing among plural pinions in planetary gears should be equal to reduce gear noise and to secure the strength of the gears and bearings. This study investigates the influence of bearing clearance on load sharing using multibody dynamics analysis. One of the characteristics of this analysis is its capability to calculate dynamic gear meshes and bearing clearance nonlinearity. Contact analysis of the gears defines the tooth surface expressed by numerical formula involving modified surface geometry. Moreover, nonlinear stiffness is used to express the bearing clearance. The numerical method is verified by experiments that measure bearing loads on pinions using strain gauges. Subsequently, the influence of bearing clearance is examined numerically. The results confirm that the clearance of the carrier is dominant. In addition, unequal loads arise from reductions in the bearing loads and inclination of the carrier. Finally, this paper suggests an appropriate clearance for well-balanced load sharing.

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A Study of the Influence of Bearing Clearance on Lateral Coupled Shaft/Disk Rotordynamics

Volume 5: Manufacturing Materials and Metallurgy; Ceramics; Structures and Dynamics; Controls, Diagnostics and Instrumentation; Education ◽

10.1115/92-gt-177 ◽

1992 ◽

Author(s):

George T. Flowers ◽

Fang Sheng Wu

Keyword(s):

Dynamical Behavior ◽

High Amplitude ◽

Bladed Disk ◽

Bearing Clearance ◽

Shaft System ◽

Coupling Dynamics ◽

Bearing Loads ◽

Rotating Flexible Disk ◽

Flexible Disk ◽

Clearance Nonlinearity

This study examines the influence of bearing clearance on the dynamical behavior of a rotating, flexible disk/shaft system. Most previous work in nonlinear rotordynamics has tended to concentrate separately on shaft vibration or on bladed disk vibration, neglecting the coupling dynamics between them. The current work examines the important rotordynamical behavior of coupled disk/shaft dynamics. A simplified nonlinear model is developed for lateral vibration of a rotor system with a bearing clearance nonlinearity. The steady-state dynamical behavior of this system is explored using numerical simulation and limit cycle analysis. It is demonstrated that bearing clearance effects can produce superharmonic vibration that may serve to excite high amplitude disk vibration. Such vibration could lead to significantly increased bearing loads and catastrophic failure of blades and disks. In addition, multi-valued responses and aperiodic behavior was observed.

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A Study of the Influence of Bearing Clearance on Lateral Coupled Shaft/Disk Rotordynamics

Journal of Engineering for Gas Turbines and Power ◽

10.1115/1.2906706 ◽

1993 ◽

Vol 115 (2) ◽

pp. 279-286 ◽

Cited By ~ 10

Author(s):

G. T. Flowers ◽

Fang Sheng Wu

Keyword(s):

Dynamic Behavior ◽

High Amplitude ◽

Bladed Disk ◽

Bearing Clearance ◽

Shaft System ◽

Coupling Dynamics ◽

Bearing Loads ◽

Rotating Flexible Disk ◽

Flexible Disk ◽

Clearance Nonlinearity

This study examines the influence of bearing clearance on the dynamic behavior of a rotating, flexible disk/shaft system. Most previous work in nonlinear rotordynamics has tended to concentrate separately on shaft vibration or on bladed disk vibration, neglecting the coupling dynamics between them. The current work examines the important rotordynamic behavior of coupled disk/shaft dynamics. A simplified nonlinear model is developed for lateral vibration of a rotor system with a bearing clearance nonlinearity. The steady-state dynamic behavior of this system is explored using numerical simulation and limit cycle analysis. It is demonstrated that bearing clearance effects can produce superharmonic vibration that may serve to excite high-amplitude disk vibration. Such vibration could lead to significantly increased bearing loads and catastrophic failure of blades and disks. In addition, multivalued responses and aperiodic behavior were observed.

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New Geometry of Generating Spiral Bevel Gear

Volume 7: 10th International Power Transmission and Gearing Conference ◽

10.1115/detc2007-34485 ◽

2007 ◽

Author(s):

Kaihong Zhou ◽

Jinyuan Tang ◽

Tao Zeng

Keyword(s):

Gear Tooth ◽

Previous Method ◽

Bevel Gear ◽

Tooth Surface ◽

Spiral Bevel Gear ◽

Surface Geometry ◽

Numerical Examples ◽

Cone Surface ◽

Spiral Bevel ◽

Involute Curve

New geometry of generating spiral bevel gear is proposed. The key idea of the new proposed geometry is that the gear tooth surface geometry can be investigated in a developed curved surface based on the planar engagement principle. It is proved that the profile curve on the back of generating cone surface is a conical involute curve. The equations of generated gear tooth surface are achieved by the conical involute curve sweeping along the tooth trace of gear. The obtained equations are explicit and independent of the machine-tool settings. This differs from previous studies. The developed theory is illustrated with numerical examples to compare with the previous method, the comparison approves that the method is possible in this way. The new method indicates that there are new solutions to the design the production of spiral bevel gear.

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Establishing gear tooth surface geometry and normal deviation

Mechanism and Machine Theory ◽

10.1016/s0094-114x(97)00075-x ◽

1998 ◽

Vol 33 (5) ◽

pp. 517-524 ◽

Cited By ~ 10

Author(s):

M.S. Shunmugam ◽

S.V.R. Surya Narayana ◽

V. Jayaprakash

Keyword(s):

Gear Tooth ◽

Tooth Surface ◽

Surface Geometry

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Comparison of planetary bearing load-sharing characteristics in wind turbine gearboxes

Wind Energy Science ◽

10.5194/wes-3-947-2018 ◽

2018 ◽

Vol 3 (2) ◽

pp. 947-960 ◽

Cited By ~ 1

Author(s):

Jonathan Keller ◽

Yi Guo ◽

Zhiwei Zhang ◽

Doug Lucas

Keyword(s):

Fatigue Life ◽

Wind Turbine ◽

Load Sharing ◽

Position Error ◽

Bearing Clearance ◽

Roller Bearings ◽

Bearing Load ◽

Tapered Roller ◽

Tapered Roller Bearings ◽

Cylindrical Roller

Abstract. In this paper, the planetary load-sharing behavior and fatigue life of different wind turbine gearboxes when subjected to rotor moments are examined. Two planetary bearing designs are compared – one design using cylindrical roller bearings with clearance and the other design using preloaded tapered roller bearings to support both the carrier and planet gears. Each design was developed and integrated into a 750 kW dynamometer tests, the loads on each planet bearing row were measured and compared to finite-element models. Bearing loads were not equally shared between the set of cylindrical roller bearings supporting the planets even in pure torque conditions, with one bearing supporting up to 46 % more load than expected. A significant improvement in planetary bearing load sharing was demonstrated in the gearbox with preloaded tapered roller bearings with maximum loads 20 % lower than the gearbox with cylindrical roller bearings. Bearing life was calculated with a representative duty cycle measured from field tests. The predicted fatigue life of the eight combined planet and carrier bearings for the gearbox with preloaded tapered roller bearings is 3.5 times greater than for the gearbox with cylindrical roller bearings. The influence of other factors, such as carrier and planet bearing clearance, gravity, and tangential pin position error, is also investigated. The combined effect of gravity and carrier bearing clearance was primarily responsible for unequal load sharing. Reducing carrier bearing clearance significantly improved load sharing, while reducing planet clearance did not. Normal tangential pin position error did not impact load sharing due to the floating sun design of this three-planet gearbox.

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Experiment of Micro-Parts Feeding on Saw-Tooth with the Effect of the Surface Geometry Parameters

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.740.99 ◽

2013 ◽

Vol 740 ◽

pp. 99-104

Author(s):

Phuong Hoai Le ◽

Thien Xuan Dinh ◽

Atsushi Mitani ◽

Shinichi Hirai

Keyword(s):

Particle Tracking ◽

Particle Tracking Velocimetry ◽

Surface Velocity ◽

Tooth Surface ◽

Characteristic Surface ◽

Surface Geometry ◽

Exciting Frequency ◽

Micro Parts ◽

Relative Scale ◽

Parts Feeding

In this work, we study experimentally the effect of the geometry parameters of saw-tooth surface and micro-part on the motion of micro-parts. The experiments are performed for a range of saw-tooth pitch,p, micro-part length,l, and exciting frequency applied to the surface,f. By the use of particle tracking velocimetry method, we can achieve time-dependent velocity, and then ensemble-averaged velocity of the micro-parts. The results show that for differentlandpbut the same relative scalel/p, the profiles of micro-part velocity against the characteristic surface velocitypfare similar. However, they shift alongpfaxis depending onp. Furthermore, the profiles are the similar for the relative scalel/pof 4 to 100. It seems that the motion of micro-part depends on characteristic surface velocitypfthan the relative scalel/pforl/plarger than a certain value.

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Nonlinear Dynamic Analysis on Planetary Gears-Rotor System in Geared Turbofan Engines

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127419500767 ◽

2019 ◽

Vol 29 (06) ◽

pp. 1950076 ◽

Cited By ~ 4

Author(s):

Lanlan Hou ◽

Shuqian Cao

Keyword(s):

Nonlinear Dynamic Analysis ◽

Period Doubling ◽

Nonlinear Behavior ◽

Rotor System ◽

Chaotic Motions ◽

Planetary Gears ◽

Gear Noise ◽

Turbofan Engines ◽

Vibration Responses ◽

Nonlinear Analytical Model

Rotor fatigue and gear noise triggered by nonlinear vibration are the key concerns in Geared Turbofan (GTF) engine which features a new configuration by introducing planetary gears into low-pressure compressor. A nonlinear analytical model of the GTF planetary gears-rotor system is developed, where the torsional effect of rotor and pivotal parameters from gears are incorporated. The nonlinear behavior of the model can be obtained by focusing on the relative torsional vibration responses between gear and rotor. The torsional nonlinear responses are illustrated with bifurcation diagrams, the largest Lyapunov exponents (LLE), Poincaré maps, phase diagrams and spectrum waterfall. Numerical results reveal that the gears-rotor system exhibits abundant torsional nonlinear behaviors, including multiperiodic, quasi-periodic, and chaotic motions. Furthermore, the roads to chaos via quasi-periodicity, period-doubling scenario, mutation and intermittence are demonstrated. The ring gear stiffness at a low value can propel the system into chaos. The damping may complicate the motion, i.e. the system may enter chaos with increasing damping. These results provide an understanding of undesirable torsional dynamic motion for the GTF engine rotor system and therefore serve as a useful reference for engineers in designing and controlling such system.

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Optimization of Profile Modifications With Regard to Dynamic Tooth Loads in Single and Double-Helical Planetary Gears With Flexible Ring-Gears

Journal of Mechanical Design ◽

10.1115/1.4031939 ◽

2015 ◽

Vol 138 (2) ◽

Cited By ~ 13

Author(s):

M. Chapron ◽

P. Velex ◽

J. Bruyère ◽

S. Becquerelle

Keyword(s):

Equations Of Motion ◽

Integration Scheme ◽

Time Varying ◽

Time Step ◽

Planetary Gears ◽

Contact Algorithm ◽

Beam Elements ◽

Internal Gear ◽

Gear Meshes ◽

Optimum Profile

This paper is mostly aimed at analyzing optimum profile modifications (PMs) in planetary gears (PGTs) with regard to dynamic mesh forces. To this end, a dynamic model is presented based on 3D two-node gear elements connected to deformable ring-gears discretized into beam elements. Double-helical gears are simulated as two gear elements of opposite hands which are linked by shaft elements. Symmetric tip relief on external and internal gear meshes are introduced as time-varying normal deviations along the lines of contact and time-varying mesh stiffness functions are deduced from Wrinckler foundation models. The equations of motion are solved by coupling a Newmark time-step integration scheme and a contact algorithm to account for possible partial or total contact losses. Symmetric linear PMs for helical and double-helical PGTs are optimized by using a genetic algorithm with the objective of minimizing dynamic tooth loads over a speed range. Finally, the sensitivity of these optimum PMs to speed and load is analyzed.

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